A WHITE Republican senator from Mississippi has apologised to people who were offended when she complimented a supporter by saying she would attend a "public hanging" if the supporter invited her.

Cindy Hyde-Smith's original remark, caught on video which was released last week, brought widespread criticism from inside and outside Mississippi, a state with a history of racially motivated lynchings.

"For anyone that was offended by my comments, I certainly apologise. There was no ill will, no intent whatsoever in my statement," Ms Hyde-Smith said during a televised debate with her African-American Democratic opponent Mike Espy.

The apology was a new approach for Ms Hyde-Smith, who repeatedly refused to answer questions about the hanging comment at a news conference on November 12, the day after the publisher of a liberal-leaning news site posted the video on Facebook and Twitter.

The clip shows Ms Hyde-Smith praising a cattle rancher at a November 2 campaign event in Tupelo by saying: "If he invited me to a public hanging, I'd be on the front row."

Shortly after the video's release, she said in a statement that the expression was an "exaggerated expression of regard" and said it was "ridiculous" to read any negative connotation into it.

"There has never been anything, not one thing, in my background to ever indicate I had ill will toward anyone," Mr Hyde-Smith, a former state agriculture commissioner, said on Tuesday night.

"I've never been hurtful to anyone. I've always tried to help everyone. I also recognise that this comment was twisted and it was turned into a weapon to be used against me, a political weapon used for nothing but personal and political gain by my opponent. That's the type of politics Mississippians are sick and tired of."

Mr Espy responded during the debate: "No one's twisted your comments because your comments were live, you know, it came out of your mouth. I don't know what's in your heart but I know what came out of your mouth.

"It went viral in the first three minutes around the world. And so it's caused our state harm. It's given our state another black eye that we don't need. It's just rejuvenated those stereotypes that we don't need any more."

Ms Hyde-Smith is the first woman to represent Mississippi in Congress. Mr Espy, a former congressman and US agriculture secretary, is seeking to become the state's first African-American senator since Reconstruction.

Hours before the debate, President Donald Trump defended Ms Hyde-Smith's "public hanging" remark, saying at the White House that she loves the people of Mississippi and the US.

"It was just sort of said in jest," Mr Trump said. "She's a tremendous woman and it's a shame that she has to go through this."

Walmart asked her to return a $2,000 campaign contribution because of the hanging remark. Walmart spokeswoman LeMia Jenkins said the company donated on November 8, three days before the release of the video.

Ms Hyde-Smith and Mr Espy each won about 41 per cent of the vote when four candidates were on the ballot on November 6. If she wins a November 27 runoff, Ms Hyde-Smith would give Republicans a 53-47 majority in the Senate.